Set up the equation for the arithmetic mean.

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ScanSolve AI Tutor · Accepted Answer

Here is the solution to question 1: a) To calculate the value of x, we use the formula for the arithmetic mean. Step 1: Set up the equation for the arithmetic mean. The arithmetic mean is the sum of the heights divided by the number of students. (1.50 + x + 1.45)/(3) = 1.60 Step 2: Solve for x. Multiply both sides by 3: 1.50 + x + 1.45 = 1.60 × 3; 2.95 + x = 4.80 Subtract 2.95 from both sides: x = 4.80 − 2.95; x = 1.85 The value of x is 1.85 m. b) i) Three main ways of describing sets are: Roster method (or Listing method): Listing all the elements of the set within curly braces, e.g., 1, 2, 3. Set-builder notation (or Rule method): Describing the properties that the elements of the set must satisfy, e.g., x x is an even number. Verbal description (or Word method): Describing the set in words, e.g., "the set of natural numbers less than 5". ii) To find n(E ∩ P), we need to identify the elements that are common to both the set of even numbers (E) and the set of prime numbers (P). Step 1: Identify the sets E and P. E = , −4, −2, 0, 2, 4, 6, (all integers divisible by 2); P = 2, 3, 5, 7, 11, (natural numbers greater than 1 with no positive divisors other than 1 and itself) Step 2: Find the intersection E ∩ P. The only number that is both even and prime is 2. So, E ∩ P = 2. Step 3: Determine the number of elements in the intersection. n(E ∩ P) is the number of elements in the set 2, which is 1. n(E ∩ P) = 1.

Set up the equation for the arithmetic mean.

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Part a· 2 steps